Word.ws English Dictionary

group rings

group rings is the plural of group ring.

Meaning of group ring

Noun

group ring (plural group rings)

  1. Given ring R with identity not equal to zero, and group G=g_1,g_2,...,g_n, the group ring RG has elements of the form a_1g_1+a_2g_2+...+a_ng_n (where a_i isin R) such that the sum of a_1g_1+a_2g_2+...+a_ng_n and b_1g_1+b_2g_2+...+b_ng_n is (a_1+b_1)g_1+(a_2+b_2)g_2+...+(a_n+b_n)g_n and the product is ∑ₖ₌₁ⁿ(∑_(g_ig_j=g_k)a_ib_j)g_k.
    Synonyms:
    group algebra

Questions about group rings

What is group rings the plural of?
Group rings is the plural of group ring.

Words near group rings in the dictionary

  1. group punishment
  2. group punishments
  3. group representation constituencies
  4. group representation constituency
  5. group ring
  6. group rings
  7. group scheme
  8. group schemes
  9. group selection
  10. group setting
  11. group sex

Source and license

Adapted from Wiktionary: group rings (page history and authors); group ring (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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